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Résumé

Tight Weyl–Heisenberg frames in l^2 (Z ) are the tool for short-time Fourier analysis in discrete time. They are closely related to paraunitary modulated filter banks and are studied here using techniques of the filter bank theory. Good resolution of short-time Fourier analysis in the joint time–frequency plane is not attainable unless some redundancy is introduced. That is the reason for considering overcomplete Weyl–Heisenberg expansions. The main result of this correspondence is a complete parameterization of finite length tight Weyl–Heisenberg frames in l^2(Z) with arbitrary rational oversampling ratios. This parame- terization follows from a factorization of polyphase matrices of paraunitary modulated filter banks, which is introduced first.

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